Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points

Xavier Buff, Arnaud Chéritat, Pascale Roesch

We prove that for all degree $d\ge 2$ and all bounded type irrational $\theta$, in the space of monic polynomials having a period $1$ Siegel disk $\Delta$ of rotation number $\theta$, the maximu…